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30 Aug 2006, 19:42
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I just had this one on a practice test and haven't seen it addressed so I thought I'd post a solution that allows one to solve it quickly. Sorry if it's a repeat. The question is:
( 1001^2 - 999^2 ) / (101^2 0 999^2 )
A) 10
B) 20
C) 40
D) 80
E) 100
My Soln:
Expand the stem to:
[(1000 + 1)(1000 + 1) - (1000 - 1)(1000-1)] / [(100+1)(100+1) - (100-1)(100-1)]
the numerator = (1,000)(1,000) + 2,000 + 1 - (1,000)(1,000) + 2,000 - 1
which = 4,000
the denominator = (100)(100) + 200 + 1 - (100)(100) + 200 - 1
which = 400
So 4,000/400 = 10 ANS A
( 1001^2 - 999^2 ) / (101^2 0 999^2 )
A) 10
B) 20
C) 40
D) 80
E) 100
My Soln:
Expand the stem to:
[(1000 + 1)(1000 + 1) - (1000 - 1)(1000-1)] / [(100+1)(100+1) - (100-1)(100-1)]
the numerator = (1,000)(1,000) + 2,000 + 1 - (1,000)(1,000) + 2,000 - 1
which = 4,000
the denominator = (100)(100) + 200 + 1 - (100)(100) + 200 - 1
which = 400
So 4,000/400 = 10 ANS A
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30 Aug 2006, 22:07
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This is a great one. I was curious about the initial problem stating "(101^2 0 999^2 )" in the denominator. Just want to make sure whether it's (101^2-99^2) or not. Given the solution, I do think 999 was just a typo. I like this one.
30 Aug 2006, 23:18
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mathec
It was discussed many times
( 1001^2 - 999^2 ) / (101^2 - 999^2 )
[(1000 + 1)(1000 + 1) - (1000 - 1)(1000-1)]---the correct formula is
(1001-999)*(1001+999)=2*(2000)IMHO it is much more easier
